Evidence of Gumbel distributions of conductance fluctuations in bacteriorhodopsin thin films

By considering a set of experiments carried out on bacteriorhodopsin in vitro by Casuso et al (2007 Phys. Rev. E 76 041919), we extract the conductance as function of the applied voltage. The microscopic interpretation of experiments shows that charge transfer is ruled by a direct tunneling (DT) mechanism at low bias and by a Fowler–Nordheim (FN) tunneling mechanism at high bias. A nucleation region at the cross-over between the DT and FN regimes can be identified. A theoretical analysis of conductance fluctuations is performed by calculating the corresponding variance and the probability density functions (PDFs): these constitute a powerful indicator in order to understand the internal dynamics of the system. Conductance fluctuations are non-Gaussian and follow well the standard generalized Gumbel distributions G.a/. In particular, at low bias, the PDFs are bimodal and can be resolved in at least a couple of G.a/ functions with different values of the shape parameter a. The nucleation region is characterized by a single Gumbel distribution, G.1/. At increasing bias, the G.1/ distribution turns in a bimodal distribution. We discuss possible correlations between the voltage dependence of the G.a/ and the microscopic mechanisms that determine the electrical response of the system.